Deployable radiator having an increased view factor

ABSTRACT

A geostationary earth orbit (GEO) spacecraft is disclosed that includes a body with north, east, south, and west sides and a north-south axis. The spacecraft has at least one deployable radiator rotatably coupled to the body. The deployable radiator has a stowed position proximate to one of the east and west sides and a deployed position that is greater than 90 degrees from the north-south axis in a direction away from the respective one of the east and west sides.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Continuation-in-Part of application Ser. No. 13/368,304 filed on Feb. 7, 2012, which is hereby incorporated in its entirety by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not Applicable.

BACKGROUND

1. Field

The present invention generally relates to Geostationary Earth Orbit (GEO) spacecraft and, in particular, relates to a non-interfering deployable radiator arrangement for GEO spacecraft.

2. Description of the Related Art

Conventionally, a GEO communications spacecraft may have deployable radiators that are stowed against the north or south spacecraft panels underneath the stowed solar arrays. The rationale for this is that the north or south panels of the spacecraft generally have the largest surface area and minimize interference with communications antennas that are mounted on the east and west sides of the spacecraft. Once in orbit and after the solar arrays have been deployed, the deployable radiators are rotated from the stowed position to the deployed position.

A drawback of this arrangement is that the deployable radiators must fit underneath the stowed solar array in the stowed position. Because of this, the deployable radiators generally include clearance cutouts and missing sections to avoid interfering with the solar array restraint mechanisms, harnessing, and/or the solar array driving mechanisms. The clearance cutouts decrease the thermal rejection capacity of the deployable radiators. In addition, the clearance cutouts complicate the design of the deployable radiators and its internal heat pipe arrangement. This deployment arrangement is more complicated, has greater potential for undesirable interferences, and is more costly to implement.

SUMMARY

The following presents a simplified summary of one or more embodiments in order to provide a basic understanding of such embodiments. This summary is not an extensive overview of all contemplated embodiments, and is intended to neither identify key or critical elements of all embodiments nor delineate the scope of any or all embodiments. Its sole purpose is to present some concepts of one or more embodiments in a simplified form as a prelude to the more detailed description that is presented later.

Various aspects of the subject technology provide a deployable radiator arrangement for GEO spacecraft in which the deployable radiators are stowed on the east and west panels of the spacecraft. This arrangement allows the deployable radiators to be deployed without interfering with solar arrays and communication antennas and without the need to incorporate cutouts in the deployable radiators, thereby improving the thermal rejection capabilities of the deployable radiators. Because clearance cutouts are not needed, the design of the deployable radiators and their respective internal heat pipe arrangement is less complicated. As a result, the deployable radiators may have a rectangular shape with a simple internal heat pipe arrangement and high radiator efficiency. The simple internal heat pipe arrangement may follow a general path within the deployable radiators without the need to accommodate clearance cutouts. In addition, the manufacture of the deployable radiators is more economical than deployable radiators used in conventional GEO spacecraft.

In addition, the deployable radiators may be positioned at an angle past the plane of the fixed north and south radiators, in other words the deployable radiator is positioned at an angle that exceeds 90 degrees. For certain aspects of spacecraft configurations, the view factor of the radiator backside to deep space is improved by positioning the radiator at an angle that exceeds 90 degrees, thereby improving the efficiency of the thermal control system.

In accordance with one aspect of the subject technology, a geostationary earth orbit (GEO) spacecraft is disclosed that includes a body having north, east, south, and west sides and a north-south axis. The spacecraft also includes at least one deployable radiator rotatably coupled to the body, the at least one deployable radiator having a stowed position proximate to one of the east and west sides and a deployed position that is greater than 90 degrees from the north-south axis in a direction away from the respective one of the east and west sides.

In accordance with one aspect of the subject technology, a method for cooling an assembly of a spacecraft is disclosed. The method includes the steps of thermally coupling the assembly to a first rigid portion of a flexible heat pipe that also has a second rigid portion that is thermally coupled to a deployable radiator coupled to a body of the spacecraft and a flexible portion coupled between the first and second rigid portions, positioning the deployable radiator in a stowed position that is proximate to one of an east or west side of the body of the spacecraft, placing the spacecraft in a GEO, and rotating the deployable radiator to a deployed position having an angle that is in the range of 90-180 degrees from a north-south axis of the body in a direction away from the stowed position.

Additional features and advantages of the subject technology will be set forth in the description below, and in part will be apparent from the description, or may be learned by practice of the subject technology. The advantages of the subject technology will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are intended to provide further explanation of the invention as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide further understanding of the subject technology and are incorporated in and constitute a part of this specification, illustrate aspects of the subject technology and together with the description serve to explain the principles of the subject technology.

FIG. 1 illustrates a GEO spacecraft with deployable radiators in a stowed position, in accordance with various aspects of the subject technology.

FIG. 2 illustrates a GEO spacecraft with deployable radiators in a deployed position, in accordance with various aspects of the subject technology.

FIG. 3 illustrates a GEO spacecraft within launch vehicle fairings, in accordance with various aspects of the subject technology.

FIG. 4A illustrates an aft-end view of a GEO spacecraft with deployable radiators in a stowed position, in accordance with various aspects of the subject technology.

FIG. 4B illustrates an aft-end view of a GEO spacecraft with deployable radiators in a deployed position, in accordance with various aspects of the subject technology.

FIG. 5 illustrates a north-facing view of a GEO spacecraft with deployable radiators in a deployed position, in accordance with various aspects of the subject technology.

FIG. 6 illustrates a heat pipe arrangement, in accordance with various aspects of the subject technology.

FIG. 7 illustrates an example of a method for cooling a GEO spacecraft, in accordance with various aspects of the subject technology.

FIG. 8 illustrates another embodiment of a GEO spacecraft with deployable radiators in another deployed position, in accordance with various aspects of the subject technology.

FIG. 9 is a plot of component temperatures vs. deployment angle, in accordance with various aspects of the subject technology.

FIG. 10 is a flow chart of an exemplary method of cooling an assembly of a spacecraft.

DETAILED DESCRIPTION

In the following detailed description, numerous specific details are set forth to provide a full understanding of the subject technology. It will be apparent, however, to one ordinarily skilled in the art that the subject technology may be practiced without some of these specific details. In other instances, well-known structures and techniques have not been shown in detail so as not to obscure the subject technology. Like components are labeled with identical element numbers for ease of understanding.

Various aspects of the subject technology provide a method for cooling a GEO spacecraft without interfering with solar arrays and communication antennas, thereby increasing the thermal rejection capabilities of the deployable radiators by minimizing clearance cutouts. In one aspect, the design of the deployable radiators and their respective internal heat pipe arrangement is less complicated, and therefore more economical, than conventional GEO spacecraft.

FIG. 1 illustrates a GEO spacecraft 100 with deployable radiators 150A-B, 160A-B in a stowed position, in accordance with various aspects of the subject technology. In some aspects, the spacecraft 100 may comprise solar arrays 120 disposed on a north 110A and/or south 110B face of the spacecraft 100. The spacecraft 100 may also comprise antenna reflectors 130 disposed on an east 110C and/or west 110D face of the spacecraft 100. The antenna reflectors 130 may be further translated toward an Earth-facing end of the spacecraft 100 to create a substantially flat region at the aft end of the spacecraft 100 for mounting of the deployable radiators 150A-B, 160A-B. In some aspects, translating the antenna reflectors 130 toward the Earth-facing end of the spacecraft 100 may require antenna feeds 135 to also be translated to maintain the proper antenna geometry. Referring to FIG. 3, the translation of the antenna feeds of the spacecraft 100 is within standard launch vehicle fairings.

First and second deployable radiators, 150A and 150B respectively, may be mounted on the east 110C face and adjacent to the aft end of the spacecraft 100 when stowed. Third and fourth deployable radiators, 160A and 160B respectively, may be mounted on the west 110D face and adjacent to the aft end of the spacecraft 100 when stowed. In one aspect, the first deployable radiator 150A may be configured to stow either on top of or under the second deployable radiator 150B. Alternatively, the first and second deployable radiators, 150A and 150B respectively, may be configured to be stowed side-by-side. In another aspect, the third deployable radiator 160A may be configured to stow either on top of or under the fourth deployable radiator 160B. Alternatively, the third and fourth deployable radiators, 160A and 160B respectively, may be configured to be stowed side-by-side. In some aspects, each deployable radiator 150A-B, 160A-B may have a width of about 3.3 ft and a length of 6.5 feet and have a total surface area of about 43 ft².

Because the deployable radiators 150A-B, 160A-B are mounted on the east 110C and west 110D face of the spacecraft 100 and adjacent to the aft end, the deployable radiators 150A-B, 160A-B have no clearance cutouts for accommodating the solar arrays 120 or the antenna reflectors 130. In some aspects, because the deployable radiators 150A-B, 160A-B have no clearance cutouts, the thermal rejection capacity of the deployable radiators 150A-B, 160A-B is higher than deployable radiators utilized in conventional GEO spacecraft that require clearance cutouts for accommodating solar arrays or antenna reflectors. For example, at roughly 40° C., an outward facing panel of the deployable radiator 150A may have a thermal rejection capability of 32 W/ft² and an inward facing panel may have a thermal rejection capability of 10 W/ft². The deployable radiators 150A-B, 160A-B may therefore each provide about 900 W of thermal rejection, thereby providing a total increase in thermal rejection for the deployable radiators 150A-B, 160A-B of about 3600 W, which for this example, represents a 50% increase in the thermal capability of the spacecraft 100.

FIG. 2 illustrates the GEO spacecraft 100 with deployable radiators 150A-B, 160A-B in a deployed position, in accordance with various aspects of the subject technology. In one aspect, the deployable radiators 150A-B, 160A-B are deployed after the spacecraft 100 has completed transfer-orbit operations, prior to entering communications service. In some aspects, the first and second deployable radiators, 150A and 150B respectively, may be configured to rotate into a north 110A and south 110B facing position, respectively, when deployed. For example, the first and second deployable radiators, 150A and 150B respectively, may rotate approximately 90 degrees from a stowed position to a deployed position either actively with a motor or actuator, or passively with a hinge and damper. In one aspect, the spacecraft 100 may comprise hinges and restraint mechanisms that are configured to secure the deployable radiators 150A-B, 160A-B for launch and facilitate deployment. In other aspects, the third and fourth deployable radiators, 160A and 160B respectively, may be configured to rotate into the north 110A and south 110B facing position, respectively, when deployed.

FIG. 4A illustrates an aft-end (anti-nadir panel) view of the GEO spacecraft 100 with deployable radiators 150A-B, 160A-B in the stowed position, in accordance with various aspects of the subject technology. In some aspects, the spacecraft 100 may further comprise first and second fixed radiators, 170A and 170B respectively, disposed on the north 110A and south 110B face of the spacecraft 100, respectively. The deployable radiators 150A-B, 160A-B may be thermally coupled to the first and second fixed radiators, 170A and 170B. For example, referring to FIG. 4B, first deployable radiator 150A may be thermally coupled to the first fixed radiator 170A. The second deployable radiator 150B may be thermally coupled to the second fixed radiator 170B. The third deployable radiator 160A may be thermally coupled to the first fixed radiator 170A. The fourth deployable radiator 160B may be thermally coupled to the second fixed radiator 170B.

FIG. 4A and 4B show heat pipes 210 connecting one of the first and second fixed radiators 170A, 170B to one of the deployable radiators 150A-B, 160A-B, with the heat pipes 210 embedded within the respective radiators. In certain embodiments, the heat pipes 210 are attached to the surface of one or more of the radiator panels 150A-B, 160A-B, 170A, and 170B, for example by bolting and bonding to the outboard faces of the respective panel. This type of attachment may simplify manufacturing and assembly of the panels and the spacecraft 100.

In certain embodiments, the heat pipes 210 may pass from one of the east deployable radiator panels 150A, 150B through or over one of the fixed radiator panels 170A, 170B to one of the west deployable radiator panels 160A, 160B. For example, a heat pipe 210 may be extend across radiator panels 150A, 170A, and 160A with flexible sections 220 between each adjacent pair of radiator panels. This embodiment may allow further sharing of the heat load/rejection between the east radiator panels 150A, 150B and the west radiator panels 160A, 160B. There are instances when the east or west side of the spacecraft 100 is subject to external solar loading while the opposite west or east is shaded, e.g., when the solar vector is approximately perpendicular to the illuminated side. In this situation, the back of the illuminated radiator will have added direct and reflected solar load in addition to added infrared backload from the thermal blankets on the illuminated side while the shaded side radiators will have no additional solar or infrared back-loading.

FIG. 5 illustrates a north-facing view of the GEO spacecraft 100 with deployable radiators 150A-B, 160A-B in the deployed position, in accordance with various aspects of the subject technology. In some aspects, a heat pipe 230 may be disposed within the fixed radiators 170A-B. In some aspects, a flexible heat pipe 210 may have a first rigid portion 210A thermally coupled to one of the fixed radiators 170A-B, a second rigid portion 210B thermally coupled to one of the deployable radiators 150A-B, 160A-B, and a flexible section 220 coupled between the first and second rigid portions 220A, 220B. In other aspects, the rigid portion 210A of flexible heat pipe 210 may be disposed within the spacecraft 100 and thermally coupled to one or more internal electronic assemblies (not visible in FIG. 2). In one aspect, the flexible sections 220 facilitate rotation of the deployable radiators 150A-B, 160A-B with respect to the fixed radiators, 170A and 170B. For example, the flexible sections 220 may flex and/or bend about 90-180 degrees to facilitate stowage and deployment. This flexible section 220 also acts to transport heat from the fixed radiator to the deployable radiator. In other aspects, the flexible section 220 may be partially embedded within the fixed radiators 170A and 170B and bonded to the heat pipe 230 and also partially embedded within the deployable radiators 150A-B, 160A-B and bonded to the heat pipe 210. In some aspects, because there are no clearance cutouts in the deployable radiators 150A-B, 160A-B, straight heat pipe sections can be used, which may increase thermal rejection performance and reduce cost.

FIG. 6 illustrates a heat pipe arrangement 200, in accordance with various aspects of the subject technology. In one aspect, an evaporator pump 250 may be configured to acquire heat and evaporate a liquid to a vapor. In some aspects, the heat pipe 235 may be configured to transport the heated vapor from the evaporator pump 250 to a colder area where heat from the heated vapor may be released, thereby condensing the vapor into a liquid. For example, the heat pipe 235 may transport the heated vapor to the deployable radiators 150A-B, 160A-B, via heat pipe 210, for cooling and condensing of the heated vapor into the liquid. The liquid may be, for example, ammonia liquid. After the vapor is condensed into the liquid, the liquid may continue along heat pipe 210, flexible section 220, and heat pipe 230 to an accumulator 240 and the evaporator pump 250 to continue the cooling cycle. The heat pipe 210, 230, and 235 may comprise smooth small diameter tubing made of aluminum or stainless steel.

Although the heat pipe arrangement 200 described above may be referred to as a loop heat pipe system (LHP), it is understood that other heat pipe arrangements may be used. For example, the heat pipe arrangement 200 may utilize flexible heat pipes arranged to connect the deployable radiator to the fixed radiator. Alternatively, a LHP system that has two connections to the deployable radiator, i.e., to the vapor side and the liquid side, may be utilized. In this example, rather than using a plurality of individual pipes, a single pipe would serpentine through the deployable panel as shown in FIG. 6.

FIG. 7 illustrates an example of a method 700 for cooling a GEO spacecraft, in accordance with various aspects of the subject technology. The method 700 comprises: mounting first and second deployable radiators on an east or west surface of the spacecraft (S702); mounting first and second fixed radiators on a north and south surface of the spacecraft, respectively (S704); thermally coupling the first and second deployable radiators to the first and second fixed radiators, respectively (S706); and deploying the first and second deployable radiators by rotating the first and second deployable radiators into a north and south facing position, respectively (S708).

FIG. 8 illustrates another embodiment of a GEO spacecraft 800 with deployable radiators 850A-B, 860A-B in another deployed position, in accordance with various aspects of the subject technology. Deploying thermal radiation panels, e.g. deployable radiators 850A-B, beyond 90 degrees with respect to a north-south axis 830 may increase the overall efficiency of the panels by increasing the view factor of the backside of the deployable radiator to deep space and decreasing the view factor blockage caused by the adjacent spacecraft elements, e.g. solar arrays, antenna reflectors, or the spacecraft body. For certain configurations of GEO spacecraft, the heat radiation performance of a deployable radiator 850A-B may be greater when deployed past the 90 degree position of the deployable radiators 150A-B shown in FIG. 2.

The example spacecraft 800 of FIG. 8 has a fixed radiator 870A on a north-facing side of the body 110. In some respects, the deployable radiators 850A-B, 860A-B are respectively rotatably coupled to the body 110 at one of the north-east, north-west, south-east, and south-west edges of the body 110. In some respects, the deployable radiators 850A-B, 860A-B are stowed in a manner similar to the configuration of the deployable radiators 150A-B, 160A-B shown in FIG. 1 for launch and are deployed generally as previously described for the deployable radiators 150A-B, 160A-B. In some respects, the deployable radiators 850A-B, 860A-B are stowed generally parallel to one of the east and west sides of the body 110. The deployable radiators 850A and 850B may be deployed to positions at angles 810A-B from the respective stowed positions. Angles 810A-B are measured from the north-south axis 830 in directions away from the stowed position of the respective deployable radiator 850A-B, as indicated by the directional arrows 810A-B. Deployable radiators 850B and 860B may be deployed to corresponding angles from their respective stowed positions on the opposite side of the body 110. In certain aspects, angles 810A and 810B may be within the range of 90-180°, as measured from a stowed position that is proximate and parallel to one of the east and west sides of the body 110. In certain aspects, angles 810A and 810B may be within the range of 90-135°. In certain aspects, angles 810A and 810B may be within the range of 130-160°. In certain aspects, the angle 810A may be different from the angle 810B.

FIG. 9 is a plot 900 of component temperatures vs. deployment angle 810A, in accordance with various aspects of the subject technology. The three curves 910, 920, 930 represent the average temperature of representative electronics assemblies (not visible in FIG. 8), identified as box #1, box #2, and box #3, of spacecraft 800, including multiple east-side antenna reflectors (not shown in FIG. 8) as simulated over an entire orbit. The electronics assemblies are coupled to flexible heat pipes 820 that are coupled to at least one of the deployable radiators 850A-B, 860A-B. It can be seen from plot 900 that boxes #1 and #2 are at approximately the same temperatures for all deployment angles 801A while box #3 runs at a lower temperature. For the example spacecraft 800, the three curves 910, 920, 930 all decrease as the deployment angle 810A increases from 90 degrees to approximately 145 degrees, then increases as the angle 810A further increases. For other configurations of spacecraft, the minimum values of the curves 910, 920, and 930 may occur at other deployment angles 810A depending on other factors such as antenna configuration, plume impingement, and mechanism limitations.

FIG. 10 is a flow chart 1000 of an exemplary method of cooling an assembly of a spacecraft. The method starts at step 1010 by thermally coupling the assembly to a first rigid portion of a flexible heat pipe, e.g. heat pipe 820 of spacecraft 800 of FIG. 8. The heat pipe 820 also has a second rigid portion that is thermally coupled to a deployable radiator, e.g. fixed radiator 870A, that is coupled to a body, e.g. body 110, of the spacecraft and a flexible portion coupled between the first and second rigid portions. The method then proceeds to step 1020 wherein the deployable radiator is positioned in a stowed position that is proximate to one of an east or west side of the body of the spacecraft. In step 1030, the spacecraft is placed in a geostationary earth orbit (GEO). Step 1030 may also include various orbital insertion and configuration operations. Step 1040 includes rotating the deployable radiator to a deployed position having an angle that is in the range of 90-180 degrees from a north-south axis of the body in a direction away from the stowed position. In certain embodiments, the deployed position may at angles in ranges of 90-135 degrees or 130-160 degrees.

The foregoing description is provided to enable a person skilled in the art to practice the various configurations described herein. While the subject technology has been particularly described with reference to the various figures and configurations, it should be understood that these are for illustration purposes only and should not be taken as limiting the scope of the subject technology.

There may be many other ways to implement the subject technology. Various functions and elements described herein may be partitioned differently from those shown without departing from the scope of the subject technology. Various modifications to these configurations will be readily apparent to those skilled in the art, and generic principles defined herein may be applied to other configurations. Thus, many changes and modifications may be made to the subject technology, by one having ordinary skill in the art, without departing from the scope of the subject technology.

It is understood that the specific order or hierarchy of steps in the processes disclosed is an illustration of exemplary approaches. Based upon design preferences, it is understood that the specific order or hierarchy of steps in the processes may be rearranged. Some of the steps may be performed simultaneously. The accompanying method claims present elements of the various steps in a sample order, and are not meant to be limited to the specific order or hierarchy presented.

Terms such as “top,” “bottom,” “front,” “rear” and the like as used in this disclosure should be understood as referring to an arbitrary frame of reference, rather than to the ordinary gravitational frame of reference. Thus, a top surface, a bottom surface, a front surface, and a rear surface may extend upwardly, downwardly, diagonally, or horizontally in a gravitational frame of reference.

A phrase such as an “aspect” does not imply that such aspect is essential to the subject technology or that such aspect applies to all configurations of the subject technology. A disclosure relating to an aspect may apply to all configurations, or one or more configurations. A phrase such as an aspect may refer to one or more aspects and vice versa. A phrase such as an “embodiment” does not imply that such embodiment is essential to the subject technology or that such embodiment applies to all configurations of the subject technology. A disclosure relating to an embodiment may apply to all embodiments, or one or more embodiments. A phrase such an embodiment may refer to one or more embodiments and vice versa.

Furthermore, to the extent that the term “include,” “have,” or the like is used in the description or the claims, such term is intended to be inclusive in a manner similar to the term “comprise” as “comprise” is interpreted when employed as a transitional word in a claim.

The word “exemplary” is used herein to mean “serving as an example, instance, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.

A reference to an element in the singular is not intended to mean “one and only one” unless specifically stated, but rather “one or more.” The term “some” refers to one or more. All structural and functional equivalents to the elements of the various configurations described throughout this disclosure that are known or later come to be known to those of ordinary skill in the art are expressly incorporated herein by reference and intended to be encompassed by the subject technology. Moreover, nothing disclosed herein is intended to be dedicated to the public regardless of whether such disclosure is explicitly recited in the above description. 

What is claimed is:
 1. A geostationary earth orbit (GEO) spacecraft comprising: a body having north, east, south, and west sides and a north-south axis; and at least one deployable radiator rotatably coupled to the body, the at least one deployable radiator having a stowed position proximate to one of the east and west sides and a deployed position that is greater than 90 degrees from the north-south axis in a direction away from the respective one of the east and west sides.
 2. The GEO spacecraft of claim 1, further comprising: at least one fixed radiator coupled to one of the north and south sides; and at least one flexible heat pipe having a first rigid portion thermally coupled to the at least one fixed radiator, a second rigid portion thermally coupled to the at least one deployable radiator, and a flexible portion coupled between the first and second rigid portions.
 3. The GEO spacecraft of claim 1, further comprising at least one flexible heat pipe having a first rigid portion disposed within the body, a second rigid portion thermally coupled to the at least one deployable radiator, and a flexible portion coupled between the first and second rigid portions.
 4. The GEO spacecraft of claim 3, further comprising at least one electronics assembly disposed within the body and thermally coupled to the fixed portion of the flexible heat pipe.
 5. The GEO spacecraft of claim 1, wherein the stowed position of the at least one deployable radiator is generally parallel to the one of the east and west sides.
 6. The GEO spacecraft of claim 1, wherein the at least one deployable radiator is rotatably coupled to the body at one of a north-east edge, a north-west edge, a south-east edge, and a south-west edge.
 7. The GEO spacecraft of claim 6, wherein the stowed position of the at least one deployable radiator is generally parallel to the one of the east and west sides.
 8. The GEO spacecraft of claim 6, wherein the deployed position has an angle from the north-south axis that is in the range of 90-180 degrees.
 9. The GEO spacecraft of claim 8, wherein the deployed position has an angle from the north-south axis that is in the range of 90-135 degrees.
 10. The GEO spacecraft of claim 8, wherein the deployed position has an angle from the north-south axis that is in the range of 130-160 degrees.
 11. A method for cooling an assembly of a spacecraft, the method comprising the steps of: thermally coupling the assembly to a first rigid portion of a flexible heat pipe that also has a second rigid portion that is thermally coupled to a deployable radiator coupled to a body of the spacecraft and a flexible portion coupled between the first and second rigid portions; positioning the deployable radiator in a stowed position that is proximate to one of an east or west side of the body of the spacecraft; placing the spacecraft in a geostationary earth orbit (GEO); and rotating the deployable radiator to a deployed position having an angle that is in the range of 90-180 degrees from a north-south axis of the body in a direction away from the stowed position.
 12. The method of claim 11, wherein the first rigid portion of the flexible heat pipe is disposed in a thermal radiator mounted to one of a north side or south side of the body of the spacecraft.
 13. The method of claim 11, wherein the first rigid portion of the flexible heat pipe is disposed within the body of the spacecraft.
 14. The method of claim 11, wherein the stowed position of the deployable radiator is generally parallel to the respective one of the east and west sides.
 15. The method of claim 11, wherein the deployed position has an angle from the north-south axis that is in the range of 90-135 degrees.
 16. The method of claim 11, wherein the deployed position has an angle from the north-south axis that is in the range of 130-160 degrees. 